Erbium-doped yttrium aluminum garnet (Er3+:YAG) rods were inserted inside undoped tubes and grown into single-crystal fibers of a diameter of 300 μm using the laser-heated pedestal growth technique. Growth at various rates resulted in radially graded distributions of Er3+ dopant ions, as observed using laser-induced fluorescence imaging. Profiles of the refractive index were measured using cross-sectional reflectometry in a microscope. Dopant distributions and the corresponding index profiles were compared with thermal diffusion theory to determine the inter-diffusion coefficient of Y3+ and Er3+ ions at 2000°C, yielding an estimated value of D=(9.10±0.8)×10-11 m2/s. This work constitutes a step toward controlled growth of fibers with high thermal conductivities, low Brillouin gain, and waveguiding properties required for high-power optical amplifier and laser applications.